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Information
| Code | CEN106 |
| Name | Mathematics 2 |
| Term | 2024-2025 Academic Year |
| Semester | 2. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ŞEHMUS FINDIK |
| Course Instructor |
1 2 |
Course Goal / Objective
To teach the student the topics of infinite series, functions of several variables, multiple integrals and integral theorems, which are the main topics of engineering mathematics, in a functional integrity.
Course Content
Sequence and series of numbers, power series, Taylor series. Quadratic curves, polar coordinates. Analytic geometry in R , vector functions. Functions of several variables, partial derivatives, minimum and maximum problems. Multiple integrals and applications. Line integral, Green's theorem. Surface integral, divergence theorem, Stokes' theorem.
Course Precondition
None.
Resources
Calculus, J. Stewart
Notes
None.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Analyzes infinite series in conjuction with convergence and divergence concepts |
| LO02 | Derives the Taylor-Maclaurin expansion of a given function. |
| LO03 | Calculates and comments on the partial derivatives of multivariable functions. |
| LO04 | Calculates multiple integrals, |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Adequate knowledge of mathematics, science and related engineering disciplines; ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Ability to identify, formulate and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice; ability to use information technologies effectively. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and conduct experiments, collect data, analyze and interpret results to investigate complex engineering problems or discipline-specific research topics. | 5 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Ability to work effectively in interdisciplinary and multidisciplinary teams; individual working skills. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Ability to communicate effectively verbally and in writing; knowledge of at least one foreign language; ability to write effective reports and understand written reports, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions. | 5 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology, and constantly renew oneself. | 5 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practice. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development. | 3 |
| PLO11 | Bilgi - Kuramsal, Olgusal | Knowledge of the effects of engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; awareness of the legal consequences of engineering solutions. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Integral applications, arc length, volume and surface area calculation | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | Parametric curves | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 3 | Polar coordinates, polar curves | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 4 | Infinite series, convergence tests | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 5 | Convergence tests (continued) | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Taylor and Maclaurin expansions, Taylor approximation | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 7 | Introduction to multivariable functions, partial derivatives and the chain rule | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Double integrals over general regions | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 10 | Triple integrals, change of variables in multiple integrals | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 11 | Double and triple integrals in polar coordinates | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 12 | Surface area calculation, line integrals | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 13 | Surface integrals, Green's theorem | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | Stokes and Divergence theorems | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 15 | FINAL | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 16 | Term Exams | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Reading the lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 122 | ||
| Total Workload / 25 (h) | 4,88 | ||
| ECTS | 5 ECTS | ||